JP2004-197660A, published by the Japan Patent Office in 2004, discloses a Homogeneous Charge Compression Ignition (to be abbreviated to HCCI hereafter) internal combustion engine comprising a first fuel injector and a second fuel injector. The first fuel injector injects fuel having a high octane value and low self-ignitability into an intake port. The injected low self-ignitability fuel is aspirated into a cylinder together with intake air to form a low self-ignitability premixed gas. The second fuel injector injects a fuel having a low octane value and high self-ignitability into the cylinder in radial fashion during a compression stroke. The injected high self-ignitability fuel is dotted through the interior of the cylinder in atomized masses, and is caused to self-ignite by compression heat. The resulting self-ignited flames propagate from a plurality of locations in the cylinder so as to burn the low self-ignitability fuel. As a result, the combustion speed increases, and combustion is completed before knocking occurs.